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A physical model is established to describe the kinetic process and the laser amplification mechanism of a diode side pumped alkali vapor laser MOPA system. The pump energy distribution inside the vapor cell is displayed. Taking into consideration the amplification saturation effect, the influences of the parameters, such as the temperature, cell length, and pump power on the output performance, are simulated and analyzed. The gain saturation effect in the direction of cell axis is also discussed. The calculations have a good agreement with observations, which shows the validity of this model. A group of optimal parameters is obtained for further improving the output characteristics of a cesium laser MOPA system.